Question

26.
A bowl contains 8 chips out of which 3 are red and 5 blue.
2 chips are drawn successively at random with replacemen t. Find
the probabilities that the first draw is a red chip and the second is
blue.

Answer 1

Answer:

The probability of the first draw being a red chip and the second being a blue chip is 15/56.

Step-by-step explanation:

From the above question,

They have given :

To calculate the probability that the first draw is a red chip and the second is blue, we can use the multiplication principle. Since the draws occur with replacement, each draw is independent and the probability of the first draw being a red chip is  $\frac{3}{8}$  and the probability of the second draw being blue is $\frac{5}{8}$ . The probability of both events occurring is $\frac{3}{8} \times \frac{5}{8}$ = $\frac{15}{64}$.

The probability of drawing a red chip on the first draw is 3/8 and the probability of drawing a blue chip on the second draw is 5/8, since the chips are returned to the bowl after each draw.

However,

       These events are not independent, since the number of red and blue chips in the bowl changes after the first draw. If the first draw is a red chip, there are only 2 red chips and 5 blue chips left in the bowl.

Therefore,

       The probability of the first draw being a red chip and the second draw being a blue chip is given by:

P(red, blue) = (3/8) * (5/7) = 15/56

So the probability of the first draw being a red chip and the second being a blue chip is 15/56.

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