The probability that a bomb hits a target 1/4. Five bombs are aimed at

1.	The probability that a bomb hits a target 1/4. Five bombs are aimed at a target. Find the probability that1. 3 bombs hit the target2. At the most 2 bombs hit the target
Answer» (1) The probability that 3 BOMBS hit the target is 45/128 (2) the probability that at most 2 bombs hit the target is 167/256 Step-by-step explanation: Let an event E be E : Bomb hits the target Then Probability of event E $P(E)=\frac{1}{4}$ Therefore, $P(\bar E)=1-\frac{1}{4}=\frac{3}{4}$ (1) Let event A be A: 3 bombs hit the target $P(A)=^5C_3(\frac{1}{4})^3(\frac{3}{4})^2$ or $P(A)=\frac{5\times 4}{2}\times \frac{9}{4^3\times 4^2}$ or $P(A)=\frac{45}{128}$ (2) Let event B be B: At most 2 bombs hit the target P(B) = 1 - Probability that 3 bombs hit the target - Probability that 4 bombs hit the target $P(B)=1-\frac{45}{128}-(\frac{1}{4})^4$ $P(B)=1-(\frac{45}{128}-\frac{1}{256})$ $P(B)=1-\frac{89}{256}$ $P(B)=\frac{167}{256}$ Hope this answer is helpful. Know More: Q: The probability that a bomb hits a target is 0.4. three bombs can destroy a BRIDGE. if in all 5 bombs are thrown find the probability that the bridge will be destroyed. Click Here: brainly.in/question/1988802 Q: The probability of a bomb hitting a target is 1/2. the least number of bombs that should be dropped to ensure that probability of the target getting bombed is at least 0.9 is: Click Here: brainly.in/question/1988793

The probability that a bomb hits a target 1/4. Five bombs are aimed at a target. Find the probability that1. 3 bombs hit the target2. At the most 2 bombs hit the target

Answer»

(1) The probability that 3 BOMBS hit the target is 45/128

(2) the probability that at most 2 bombs hit the target is 167/256

Step-by-step explanation:

Let an event E be

E : Bomb hits the target

Then

Probability of event E

$P(E)=\frac{1}{4}$

Therefore,

$P(\bar E)=1-\frac{1}{4}=\frac{3}{4}$

(1) Let event A be

A: 3 bombs hit the target

$P(A)=^5C_3(\frac{1}{4})^3(\frac{3}{4})^2$

or $P(A)=\frac{5\times 4}{2}\times \frac{9}{4^3\times 4^2}$

or $P(A)=\frac{45}{128}$

(2) Let event B be

B: At most 2 bombs hit the target

P(B) = 1 - Probability that 3 bombs hit the target - Probability that 4 bombs hit the target

$P(B)=1-\frac{45}{128}-(\frac{1}{4})^4$

$P(B)=1-(\frac{45}{128}-\frac{1}{256})$

$P(B)=1-\frac{89}{256}$

$P(B)=\frac{167}{256}$

Hope this answer is helpful.

Know More:

Q: The probability that a bomb hits a target is 0.4. three bombs can destroy a BRIDGE. if in all 5 bombs are thrown find the probability that the bridge will be destroyed.

Click Here: brainly.in/question/1988802

Q: The probability of a bomb hitting a target is 1/2. the least number of bombs that should be dropped to ensure that probability of the target getting bombed is at least 0.9 is:

Click Here: brainly.in/question/1988793