Hello all, Could use some help with this problem. Can\'t figure it out: An accid

Question

Hello all,

Could use some help with this problem. Can't figure it out:


An accident victim will die unless in the next 10 minutes he receives some type A, Rh-positive blood, which can be supplied by a single donor. The hospital requires 2 minutes to type a prospective donor's blood and 2 minutes to complete the transfer of blood. Many untyped donors are available, and 40% of them have type A, Rh positive blood. What is the probability that the accident victim will be saved if only one blood-typing kit is available? Assume that the typing kit is reusable but can process only one donor at a time.


Thanks in advance!

Eric

Explanation / Answer

so we have total 8 min to correctly type a donor.

probability that 1st donor matches is P1 = 0.4

probability that 1st donor does not match, 2nd donor matches is

P2 = (1-0.4)(0.4)

similarily, we have

P3= (1-0.4)(1-0.4)(0.4)

P4=(1-0.4)3 (0.4)

P = P1+P2+P3+P4

= 0.4[1+(0.6) + (0.6)2 + (0.6)3 ] = 0.87

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