The next generation of miniaturized wireless capsules with active locomotion wil

Question

The next generation of miniaturized wireless capsules with active locomotion will require two miniature electric motors to maneuver each capsule. Suppose 10 motors have been fabricated but that, in spite of tests performed on the individual motors, 2 will not operate satisfactory when placed in a capsule.

To fabricate a new capsule, 2 motors will be randomly selected(that is, each pair of motors has the same chance of being selected.)

Find the probability that:

A: Both motors will operate satisfactory in the capsule.

B:One motor will operate satisfactory in the capsule and one will not.

Explanation / Answer

Probability that a motor will operate successfuly = 8/10 = 0.8

Probability that a motor will not operate successfully = 2/10 = 0.2

A. Probability that both motors will operate successfully = 0.8 * 0.8 = 0.64.

B, Probability that the first motor will operate satisfactory in the capsule and the second will not

= 0.8 * 0.2 = 0.16

Probability that the second motor will operate satisfactory in the capsule and the first will not

= 0.2 * 0.8 = 0.16

=> Probability that one motor will

Probability that the first motor will operate satisfactory in the capsule and the other will not

= 0.16 + 0.16 = 0.32

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