Question

Deepak has 25% chance of winning each hand of black jack he plays.If he has $150 and bets$50 a hand .what is the probability that he will still have money after the 3rd hand? Please help me for solving this problem... @ estudier

Answer 1

Think of the various possibilities (define the event space).

Answer 2

sorry I have no idea at all can you explain in detail

Answer 3

Maybe think of it like this:
Hand 1 starts with $150
... 25% +50$
... 75% -50$

Hand 2 either starts with 200$ or 100$
... 25% +50$
... 75% -50$

Hand 3 can start with 250$ (if won twice in a row), 150$ if won once and lost once, or 50$ if lost twice in a row.
... 25% +50$
... 75% -50$

Hand 3 can end with 300$ (won 3 times), 200$ (2 wins, 1 loss), 100$ (1 win, 2 losses), or 0$ (3 losses in a row).

Answer 4

I am sorry the answer option is A.1/64 B.3/16 C.27/64 D.37/64 E.3/4

Which of these will come?

Answer 5

And my doubt is hw will get this?

Answer 6

We see that there are three ways to still have money, and one way to have nothing left after three hands.
You'll use multiplication rule on each of those three ways, then addition rule to combine them.

Answer 7

Multiplication Rule.
Way one: win AND win AND win
Way two: win AND win AND lose
Way three: win AND lose AND lose

The probability of winning is 0.25 and of losing is 0.75.

Way one is 0.25 × 0.25 × 0.25
Way two is 0.25 × 0.25 × 0.75
Way three is 0.25 × 0.75 × 0.75

Answer 8

You can also simply find the probability of losing three times in a row and subtract that from 1.

That is the subtraction rule using the complement (it is often the best way to go in situations like this, but I wanted to show you the long way too, so you'll understand how this all works).

Answer 9

Understand so far?

Answer 10

yup

Answer 11

then how fraction will come?

Answer 12

If you do it the long way, the total probability is
the sum of way one OR way two OR way three.
That is the addition rule, when you have an OR situation, you add probabilities.

Answer 13

Try that, then we'll compare with the shortcut using the complement.

Answer 14

Oh, one more important detail that I forgot: There is only one way to win three times in a row, but there are three ways each to win once and lose twice and to win twice and lose once, so you have to multiply the probabilities for ways two and three by 3 to get their totals.

That's the combination rule.

Answer 15

Can you show me how to do this?

Answer 16

I'd like to see you try it first. Read through what I told you again, and put the steps together.