Assume that when blood donors are randomly selected, 40% of them have blood that is Type O  (i need help with stats)?

(i) If we randomly select 8 blood donors, find the probability that exactly three donors have Type O blood. (ii) Based on the four requirements for binomial distribution, justify that the above situation is a binomial distribution. (ii) If 36 blood donors are randomly selected, find the probability that exactly 14 donors have Type O blood.

1 Answer

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  • 8C4 * 0.4^4 * (1 - 0.4)^(8 - 4) =>

    (8! / (4! * (8 - 4)!)) * 0.4^4 * 0.6^4 =>

    (8 * 7 * 6 * 5 * 4! / (4! * 4!)) * (0.4 * 0.6)^4 =>

    (8 * 7 * 6 * 5 / 24) * 0.24^4 =>

    8 * 7 * 6 * 5 * (24/100)^4 / 24 =>

    8 * 7 * 6 * 5 * 24^3 / 100^4 =>

    8 * 7 * 6 * 5 * (2^3 * 3)^3 / 10^8 =>

    8 * 7 * 6 * 5 * 2^9 * 3^3 / 10^8 =>

    8 * 7 * 6 * 2^8 * 3^3 / 10^7 =>

    2^11 * 2 * 3^4 * 7 / 10^7 =>

    2^12 * 3^4 * 7 / 10^7 =>

    2^12 * 81 * 7 / 10^7 =>

    2^12 * 567 / 10^7 =>

    2^11 * 1134 / 10^7 =>

    2^10 * 2268 / 10^7 =>

    2^9 * 4536 / 10^7 =>

    2^8 * 9072 / 10^7 =>

    2^7 * 18144 / 10^7 =>

    2^6 * 36288 / 10^7 =>

    2^5 * 72576 / 10^7 =>

    2^4 * 145152 / 10^7 =>

    2^3 * 290304 / 10^7 =>

    2^2 * 580608 / 10^7 =>

    2 * 1161216 / 10^7 =>

    2322432 / 10^7 =>

    0.2322432

    36C14 * 0.4^14 * (1 - 0.4)^(36 - 14) =>

    (36! / (14! * 22!)) * 0.4^14 * 0.6^22 =>

    ‭0.1341305148653602187064091242135...

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