Binomial Distribution

Question

1) The incidence of an occupassional disease in an industry in such that the workers have 20% chance of suffering from it. what is the probability that out of 6 workers 4 or more will catch the disease.?

2) seven dice are thrown 729 times how many times do you expect atleast 4 dice to show 3 or 5 ?

Answer 1

1)

p = 0.2 n = 6, r = 4, 5, 6

use binomial formula to compute probability r = 4, 5, 6

p(r = 4) = C(6,4) * 0.2^4 * 0.8^2

p(r = 5) = C(6,5) * 0.2^5 * 0.8^1

p(r = 6) = C(6,6) * 0.2^7 * 0.8^0

sum probabilities to get answer.

6 possible values for a dice, so probability of getting 3 or 5, is 2/6 or 1/3 = 0.333

n = 7, p = 1/3, r = 4, 5, 6, 7

use binomial formula to compute probability r = 4, 5, 6, 7

p(r = 4) = C(7,4) * 0.333^4 * 0.667^3

p(r = 5) = C(7,5) * 0.333^5 * 0.667^2

p(r = 6) = C(7,6) * 0.333^6 * 0.667^1

p(r = 7) = C(7,7) * 0.333^7 * 0.667^0

sum probabilities to get probability that 4 or more dice out of 7 will have a 3 or 5.

multiply that probability times 729 to get the number of times you expected a roll of 7 dices will have a 3 or a 5.