Question #44fbc
1 Answer
The probability that at most three of them are black
Explanation:
Given-
Number of black buttons
Number of brown buttons
Total buttons
If one button is taken at random the probability of it to be black
#p=0.5#
#q=1-0.5=0.5#
In five tries, we take five buttons, we expect the following results
3 black and 2 brown
Or
2 black and 3 brown
Or
1 black and 4 brown
It is like tossing five coins, with known probability, is tossed and expect 3 or 2 or 1 head.
Use the binomial formula
#P_((r))=""^nC_r.p^r.q^(n-r)#
3 black and 2 brown
#P_((r=3))=""^5C_3xx0.5^3xx0.5^(5-3)=10 xx 0.125xx0.25=0.3125#
2 black and 3 brown
#P_((r=2))=""^5C_2xx0.5^2xx0.5^(5-2)=10 xx0.25xx0.125=0.3125#
1 black and 4 brown
#P_((r=1))=""^5C_1xx0.5^1xx0.5^(5-1)=5xx0.50 xx 0625=0.1563#
The probability that at most three of them are black
