Question

7. A box contains 5 blue and 8 green balls .If two balls are selected at random from this box,what is the probability that
1. They are both blue
2. Both green
3. 1 blue and 1 green.​

Answer 1

Answer:

The probability of the given events is:

1. Both are blue $=0.128$
2. Both are green $=0.358$
3. One blue and one green $=0.5$

Explanation:

The probability of an event is calculated using the formula:

$P(A)=\frac{n(A)}{n(S)}$

where P(A) is the probability of an event A,

n(A) is the number of favorable outcomes,

n(S) is the total number of outcomes.

Step-by-step explanation:

Step-1:

We are given that there are $5$ blue and $8$ green balls in a box.

There are a total of $13$ balls in a box.

Step-2:

(a) The probability to draw a blue ball on the first draw is $P(Blue)=\frac{5}{13}$

The probability to draw a blue ball on the second draw is $P(Blue)=\frac{4}{12}$

Therefore, the probability that two balls drawn at random are both blue is

$P(BothBlue)=\frac{5}{13}*\frac{4}{12}\\P(BothBlue)=0.128$

Step-3:

(b) The probability to draw a green ball on the first draw is $P(Green)=\frac{8}{13}$

The probability to draw a green ball on the second draw is $P(Green)=\frac{7}{12}$

Therefore, the probability that two balls drawn at random are both green is

$P(BothGreen)=\frac{8}{13}*\frac{7}{12}\\P(BothGreen)=0.358$

Step-4:

(c) We have to find the probability of drawing one blue and one green

This can be done in two ways.

Case I:

The probability to draw a blue ball on the first draw is $P(Blue)=\frac{5}{13}$

The probability to draw a green ball on the second draw is $P(Green)=\frac{8}{12}$

Case II:

The probability to draw a green ball on the first draw is $P(Green)=\frac{8}{13}$

The probability to draw a blue ball on the second draw is $P(Blue)=\frac{5}{12}$

Therefore, the two cases will be added:

The probability of drawing one blue and one green ball is

$P(A)=\frac{5}{13}*\frac{8}{12}+\frac{8}{13}*\frac{5}{12}\\P(A)=0.25+0.25\\P(A)=0.5$

Therefore, the probability of drawing one blue and one green ball is $0.5$

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