Question

3. There are 20 black cell phones and 30 white cell phones in a store. An employee t phones at random. Find the probability that (a) there will be exactly 4 black cell phones among the chosen phones; (b) there will be less than 3 black cell phones among the chosen phones.

Answer 1

$\\\\ Total\ number\ of\ phone =20+30=50\\ Number\ of\ way\ of\ choosing\ 10\ phone \ out\ of\ 50\ phone = ^{50}C_{10}\\ \\ \\\ (a)\ Number\ of\ way\ of\ choosing\ exactly\ 4\ black \ cell\ phone = ^{20}C_4\times ^{30}C_6\\ \\ Hence\ probability =\frac{^{20}C_4\times ^{30}C_6}{^{50}C_{10}}=0.28\\ \\ {(b)\ Number\ of\ way\ of\ choosing\ less\ than \ 3\ black \ cell \ phone=^{20}C_0\times ^{30}C_{10}+^{20}C_1\times ^{30}C_9+^{20}C_2\times ^{30}C_8}\\ \\ Hence\ probability =\frac{^{20}C_0\times ^{30}C_{10}+^{20}C_1\times ^{30}C_9+^{20}C_2\times ^{30}C_8}{^{50}C_8}=0.1390$