some probability questions

[manasi4gre]

1. In how many orders may a coin show 3 tails & 2 heads after being tossed 5 times?

2. Suppose we know there aew 3 tails and 2 heads, what is the probability that the order is exactly HTHTT?

3. Three cards are drawn from a deck of playing cards without replacement.
Find probability that there are 1 picture card and 2 aces in that order?

[samy_dg]

1. In how many orders may a coin show 3 tails & 2 heads after being tossed 5 times?
Required no. of ways= No. of ways in which the 3 heads (or the 2 tails) can be chosen out of the 5 tosses.
= 5C3( or 5C2) = 10.

2. Suppose we know there are 3 tails and 2 heads, what is the probability that the order is exactly HTHTT?
p= (.5)^5 = 1/32
probability of each outcome is .5; the combined probability is their product( as the events are independent)


3. Three cards are drawn from a deck of playing cards without replacement.
Find probability that there are 1 picture card and 2 aces in that order?
(12/52)*(4/51)*(3/50)

[arjmen]

For Q2, I'd vote 1/10 since we know that there are 3 tails and 2 heads - which can be ordered in 10 ways - and [HTHTT] is 1 way of ordering them.

[Dimas]

Agreed with arjmen.

[manasi4gre]

Thanks for your answers everyone..

The correct answer stands as:

1) 10
2) 1/10

As for the third, can anyone tell me what is a picture card?
Does it refer to the face cards?

[dsaqwert]

As for the third, can anyone tell me what is a picture card?
Does it refer to the face cards?

king, queen and jack

[manasi4gre]

dsaqwert,
yeah, the face cards are king, queen and jack.

But what are the 12 picture cards?

[dsaqwert]

dsaqwert,
yeah, the face cards are king, queen and jack.

But what are the 12 picture cards?

3*4=12
king, queen and jack of spades; king, queen and jack of hearts; king, queen and jack of diamonds; king, queen and jack of clubs

[manasi4gre]

Thx, dsaqwert.. So these are the 12 picture cards...and the face cards are 52 in number..am I right?

[arjensteve]

picture card or a face card refers to a king,queen or jack (which have faces,pictures on them)