Question

Q. A box contains 10 red and 12 white rose flowers. Flowers are picked up at random one by one without replacement. What is the probability that
(i) First 3 flowers are red
(ii) There are 2 red and 3 white flowers
In the first four picked up.
(iii) The third one is red given that the first 2 are white

Answer 1

Answer on Question #59816 – Math – Statistics and Probability

Question

A box contains 10 red and 12 white rose flowers. Flowers are picked up at random one by one without replacement. What is the probability that

(i) First 3 flowers are red

(ii) There are 2 red and 3 white flowers

In the first four picked up.

(iii) The third one is red given that the first 2 are white.

Solution

(i) Probability that the first 3 flowers are red: $P = \frac{10}{22} \times \frac{9}{21} \times \frac{8}{20} = 0.078$;

(ii) Statement 'There are 2 red and 3 white flowers in the first four picked up' is incorrect;

(iii) The third one is red given that the first 2 are white:

P('the third one is red'|'the first two are white') = $\frac{P(\text{the third one is red}', \text{the first two are white}')}{P(\text{the first two are white}')} = \frac{\frac{12 \cdot 11 \cdot 10}{22 \cdot 21 \cdot 20}}{\frac{12 \cdot 11}{22 \cdot 21}} = \frac{10}{20} = 0.5$.

Answer: (i) 0.078; (ii) - ; (iii) 0.5.

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