Please help me with my math homework?
) From a box containing blue balls and green balls, balls are drawn in succession. What is the probability that all are of the same color if:
a) there is replacement?
b) there is no replacement?
) Assume that there is an equal chance for a baby to be a girl or a boy. If a family has children,find the probability that both children are boys if:
a) the older child is a boy
b) at least one of the children is a boy
) A box contains red balls and white balls. Two balls are drawn in succession.
Find the following probabilities if the balls are drawn with replacement:
a) A red ball is drawn, then another red ball is drawn.
b) A red, then a white ball is drawn.
c) Two white balls are drawn.
d) Both balls are of the same color.
Answer
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) With replacement, the probability of drawing any particular color remains constant over the draws.
The box contains balls in total.
a) The probability of drawing blue three times in a row is the number of blue balls divided by the number of total balls.
P(b) = /.
The probability of doing this three times in a row is / * / * / = / = .
Similarly, the probability of drawing three greens is / * / * / = / = .
The total probability of all draws the same color is . + . = .
b) Without replacement, the numerator and denominator both change.
Blue: P(b,b,b) = / * / * / = .
Green: P(g,g,g) = / * / * / = .
The total probability = . + . = .
) The possible choices for the sexes of two children are
B,B
B,G
G,B
G,G
Let’s assume the first entry is the older child.
a) There are two cases where the older child is a boy. Only one of those cases has both children as boys, so the probability that both children are boys, given that the older child is a boy is %.
b) There are three cases where at least one child is a boy. Of these, only one has boys for both children. The probability that both children are boys is /.
) Sampling with replacement means the numerators and denominators stay constant.
There are total balls. The chance of drawing a red ball is /, the chance of drawing a white one is /.
a) P(r,r) = / * / = /
b) P(r,w) = / * / = /
c) P(w,w) = / * / = /
d) P(both same color) = P(r,r) + P(w,w) = ( + ) / = /