Question

4. A fair coin is flipped 6 times.

a. what is the distribution of outcomes?

b. what is the probability of getting 4 heads/2 two tails in six flips of a coin?

Answer #1

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a.

We use the binomial distribution to get the distribution of x with a binomial distribution with p = .50, and n = 6 ( 6 rolls of dice). Outcome is getting a head ( tail will also be the same)

a. Distribution of outcomes | |

Number of Heads(x) | p(x) |

0 | 0.01563 |

1 | 0.09375 |

2 | 0.23438 |

3 | 0.31250 |

4 |
0.23438 |

5 | 0.09375 |

6 | 0.01563 |

b.

As in the table, probability of 4 Heads , 2 Tails is 0.23438 ( highlighted in table p(x=4))

**Answer: 0.23438**

A coin is flipped. If a heads is flipped, then the coin is
flipped 4 more times and the number of heads flipped is noted;
otherwise (i.e., a tails is flipped on the initial flip), then the
coin is flipped 2 more times and the result of each flip (i.e.,
heads or tails) is noted successively. How many possible outcomes
are in the sample space of this experiment?

A fair coin is flipped is 6 times. What is the probability that
there were more head in the first 3 flips than in the last 3
flips?

Given a fair coin, if the coin is flipped n times, what is the
probability that heads is only tossed on odd numbered tosses.
(tails could also be tossed on odd numbered tosses)

When coin 1 is flipped, it lands on heads with probability
3
5
; when coin 2 is flipped it lands on heads with probability
4
5
.
(a)
If coin 1 is flipped 11 times, find the probability that it
lands on heads at least 9 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the...

An unfair coin is flipped 3 times, heads is 4 times as likely to
occur than tails.
x= the number of heads.
Find the probability distribution, E(x), and σ(x).

When coin 1 is flipped, it lands on heads with probability
3/5 ; when coin 2 is flipped it lands on heads with probability
4/5 .
(a)
If coin 1 is flipped 12 times, find the probability that it
lands on heads at least 10 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the first of...

A fair coin is flipped six times. Find the probability that
heads comes up exactly four times.
1/16
15/64
90/16
1/4
2/3

1. In this problem, a fair coin is flipped three times. Assume
that a random variable X is defined to be 7 times the number of
heads plus 4 times the number of tails.
How many different values are possible for the random variable
X?
2. Fill in the table below to complete the probability density
function. Be certain to list the values of X in ascending
order.
Value of X | Probability

In this problem, a fair coin is flipped three times. Assume that
a random variable X is defined to be 7 times the number of heads
plus 4 times the number of tails.
How many different values are possible for the random variable
X?

You have a coin that is not weighted evenly and therefore is not
a fair coin. Assume the true probability of getting heads when the
coin is flipped is 0.52 Find the probability that less than 76 out
of 157 flips of the coin are heads.

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