You roll a fair 6-sided die, and then flip a coin as manytimes as the value of t

Question

You roll a fair 6-sided die, and then flip a coin as manytimes as the value of the roll (for example, if you roll a 3, youflip the coin 3 times). You count the number of heads. A) Are the number of heads and the value of the die rollindependent? Why or why not? B) If you roll a 4, what is the probability of getting all 4heads? C) Without knowing what you roll yet, what is the probabilityof getting all heads?   Please show how you got the answer!! Thanks!! You roll a fair 6-sided die, and then flip a coin as manytimes as the value of the roll (for example, if you roll a 3, youflip the coin 3 times). You count the number of heads. A) Are the number of heads and the value of the die rollindependent? Why or why not? B) If you roll a 4, what is the probability of getting all 4heads? C) Without knowing what you roll yet, what is the probabilityof getting all heads?   Please show how you got the answer!! Thanks!!

Explanation / Answer

a). assuming its a fair die and coin, so head has 1/2 probability, and 1-6 on the die has 1/6chances. the number of times i get to flip the coin is depends on the numberi got from rolling the die, since the chances from the die israndom, and the chance of getting heads are random, so they areindependent. b). roll a 4, i get to clip the coin for 4 times. p(head)=1/2 p(4 heads)=1/2*1/2*1/2*1/2=(1/2)^4=0.0625 c). P(getting all heads)=(1/2)^n where n is the number got from the die

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