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Altogether there are 12 counters

the probability of a black counter is

3/12

the probability of a red counter is

4/12

Because the questions asks for a black OR red counter

we have to apply the or real which states you add the probabilities rather than times which is the and rule

therefore 3/12 + 4/12 = 7/12

number of counters in the bag = 3 + 4 + 5 = 12
so the probability of getting red counter equals the number of red counters in bag divided by the total number of counters
P(red) = 4 / 12 = 1/3
and we can do the same for P(black)
P(black) = 3 / 12 = 1 / 4

P(Red) = 4/12 = 1/3

P(Black) = 3/12 = 1/3

When i say P(Black) i mean what is the probability that the counter is black

Total number of counters = 3+4+5=12

probability of picking a black counter, P(black) = 3/12

probability of picking a red counter,  P(red) = 4/12

probability of picking a blue counter, P(blue) = 5/12

'and' means multiply the probabilities stated

'or' means add the probabilities stated

so probability that a black or red counter is taken =

P(black) + P(red)=  3/12 + 4/12 = 7/12

Total number of counters is 12 so 1/12 chance of picking any counter.
3 black counters therefore there's a 3/12 chance of picking a black counter.
4 red counters therefore there's a 4/12 chance of picking a red counter
5 blue counters therefore there's a 5/12 chance of picking a blue counter

Question states the probability of a black OR a red counter, note the keyword

OR means you need to add the probabilities because you've got the probability of picking any of the black counters aswell as the probability of picking all of the red counters.

Therefore you'd do 3/12 + 4/12 = 7/12 probability.

3 black + 4 red = 7 counters that are black or red

Total number of counters = 3+4+5= 12 counters

probability = outcome we want / total possible outcomes

prob = 7/12 chance of a black or red counter

Total number of counters = 3+4+5=12

probability of picking a black counter, P(black) = 3/12

probability of picking a red counter,  P(red) = 4/12

probability of picking a blue counter, P(blue) = 5/12

'and' means multiply the probabilities stated

'or' means add the probabilities stated

so probability that a black or red counter is taken =

P(black) + P(red)=  3/12 + 4/12 = 7/12

Firstly, you would need to calculate the total number of counters in the bag. There are 3 black, 4 red and 5 blue. To calculate the total number of counters,we add this all together: 3+4+5=12, so the total number of counters in the bag is 12.

The key aspect here is that it asks you to calculate the probability that the counter is black OR red. This means you must find the number of black and red counters in the bag. In this case, it's 7 (3+4).

You then divide this number (n) by the total number of counters (#). So probability (P) = n/#.

So P = 7/12.

3+4+5 = 12 (this is the total amount of counters)

3+4= 7 (total of red and black counters)

7/12 (this is the simplest fraction of counters that are red or black)

total ways of taking a counter =12 different ways(as there is total 12 balls)

total ways of taking a black counter=3

total ways of taking a red counter=4

total ways of taking a black or red=3+4=7

probabilty of (black or red)=7/12

There are 3 black counters and 4 red counters and 12 counters of any colour altogether. When you get the probability of choosing either a red or a black  the probability is 4+3 = 7/12

7 out of 12

Total number of counters 12

P(BL or R)=P(BL) + P(R)

P(BL or R)=3/12 + 4/12

P(BL or R)=7/12

Knowledge Required Beforehand:

1) Whenever you are asked to find the "Probability of an event A OR Probability of another event  B", just add the favorable outcomes of event A and event B.

Using this, in the question given above, the number of favorable outcomes = no. of black counters + no. of red counters = 3 + 4 = 7

2) One must also find the total number of possible outcomes.

For our problem total number of possible outcomes = number of Black Counters + number of red Counters + number of Blue Counters = 3 + 4 + 5 = 12.

3) P (E) = Number of Favorable Outcome ÷ Total Number of Possible Outcomes, where: P(E) stands for Probability of the event.

Actual Solution:

P (Black or Red Counter) =  Number of Black Or Red Counter ÷ Total Number of Possible Outcomes = 7÷12  = 0.58 (approximately).

Total no. of counters=12

Prob. of a black counter =3/12

Prob. of a red counter=4/12

And the probability of a counter being red and black is 4/12+3/12=7/12.

Probability = (Possibilities with right outcome) / (Total possibilities)

Possibilities with right outcome = "How many are 'black or red' "

Total possibilities = "How many counters in total"

Answer will be a fraction / decimal between 0 (never happens) and 1 (always happens).

Hope this helps.