Question

1. Amy rolls a 6-sided die 10 times. What is the probability that 3 specified rolls are 6s and none of the others is an 6? answer 0.0013

2. Amy tosses 90000 biased coins. Each coin comes up heads with probability 0.7. What is the probability that exactly 4 of the last 9 coins come up heads? answer 0.0735

3. Amy rolls a 6-sided die 20000 times. What is the probability that exactly 4 of the last 12 rolls are 9s? answer 0.0888

4. Amy shoots 8 arrows at a target. Each arrow hits the target (independently) with probability 0.7. What is the probability that exactly 5 of the arrows hit the target and the others miss? answer 0.2541

5. Amy shoots 9 arrows at a target. Each arrow hits the target (independently) with probability 0.8. What is the probability that 6 specified arrows hit the target? answer 0.2621

6. Amy rolls a 6-sided die 11 times. If exactly 3 of the rolls are 8s, what is the probability that 3 specified rolls are 8s and none of the others is an 8? answer 0.0061

Answer 1

S1. P(6) = % P( Ceetteug Exactly 3 solls as 6 on Specified otls): (E)-0.0012] - Plē)= 5//6 :- PCH)= 0. P(T)= 1-P(H) 0.3 . Pl Exactly 4 heads out of 9 toss) = (2Xecu»°c oern} = Q )(0.75'C0.33 -0.0735) %3D (3 * ResulLE should not be 9 but any no beteveen 1 bo 6. Pob of a= %, Isas6 Pla)= V6, pla)= 5/6 %3D P( Exactly 4 times 'a' in last 12 rolls) )( 0.0 888 %3D O P(Hit) = P(H)= 0,7, P(A)= 0.3 P(5 success in 8 trials): (8)co.70.3 0.2541 O PLH)= 0.8, P(A)=0,2 Arrows are &pecified, P(G Hit out of= 0.002) However if only specified targeks considered, reqt prob=(0.8)': b.2621) 6 Again: - Dice can't reselt in an 8 for any ether no a, pla)= : 0.006|| (5/j8 . Regd prob= (11,3) ( k