Question

15. A box contains 10 bulbs, of which three are defective. If a random sample of 5 bulbs is drawn, find the probabilities that the sample contains (i) Exactly 2 defective bulbs (ii) At the most 1 defective bulb.​

Answer 1

Answer:

ii)

Step-by-step explanation:

atmost 1 defective bulb

Answer 2

Given:

A box contains 10 bulbs, of which three are defective. If a random sample of 5 bulbs is drawn,

To Find:

find the probabilities that the sample contains (i) Exactly 2 defective bulbs (ii) At the most 1 defective bulb.​

Solution:

Total bulbs are 10, defective ones are 3 and the normal ones are 7. Before solving this question we should know that when we select r objects out of n objects then we use the formula nCr, now moving ahead

(i) Probability if exactly 2 bulbs are defective,

$P=\frac{^3C_2*^7C_3}{^{10}C_5}\\=\frac{3*35}{252}\\=\frac{5}{12}$

Hence, the probability to get exactly 2 defective bulbs is 0.4167.

(ii) Probability If at most 1 defective bulb is selected,

$P=\frac{^3C_0*^7C_5}{^{10}C_5} +\frac{^3C_1*^7C_4}{^{10}C_5} \\=\frac{1}{12} +\frac{5}{12} \\=\frac{1}{2}$

Hence, the probability that at most 1 defective bulb is selected is 0.5.