Final answer:
The probability of exactly two bombs striking the target and at least two bombs striking the target were calculated using the binomial probability formula. The provided options, however, do not match these calculations, indicating there could be a misunderstanding or error in the probability value given in the question.
Step-by-step explanation:
The probability that a bomb dropped from an envelope will strike a certain target is 51. To calculate the probability of exactly 2 striking the target using the binomial probability formula, we can use the fact that there are 6 bombs, or trials, and we want exactly 2 successes (hits):
P(exactly 2 hits) = 6C2 * (1/5)2 * (4/5)4
= 15 * (1/25) * (256/625)
= 15 * (256/15625)
= 3840/15625
This matches none of the given options, indicating there might be an error in the provided choices or in the statement of the probability of a strike being 51.
For part (ii), calculating the probability of at least 2 hits, we look at the complement of having 0 or 1 hits:
P(at least 2 hits) = 1 - P(0 hits) - P(1 hit)
= 1 - [6C0 * (1/5)0 * (4/5)6] - [6C1 * (1/5)1 * (4/5)5]
= 1 - [(4/5)6] - [6 * (1/5) * (4/5)5]
Again, this calculation does not appear to match the given options, suggesting there might be an error in the question or options.